Remove ice cream from freezer and let sit at room temperature for 3-4 minutes until slightly softened but still firm. This makes blending easier without melting.
Add ice cream to blender first, followed by 1/4 cup of the cold milk, vanilla bean paste, and vanilla extract.
Pulse 4-5 times to break down the ice cream into chunks, then blend on medium speed for 20-30 seconds until smooth and creamy.
Check consistency by lifting the blender lid — the shake should slowly fall from a spoon. If too thick, add remaining milk 1 tablespoon at a time and pulse briefly.
Pour immediately into chilled glasses and serve with wide straws. The shake will continue to thicken as it sits.